Analysis of multi-stage production/inventory system with an acceptable response time

This paper describes a method to decide the inventory levels of semifinished and finished products so as to realize the target service rate by shipping the finished products within a specified time which we call the acceptable response time. We analyze the substitution relation between the acceptable response time and the inventory levels of semifinished and finished products. As a result, inventory levels required according to the length of the acceptable response time under the condition of satisfying the target service rate are obtained. The validity of our method is also demonstrated through simulation experiments with the conditions given by the analysis.     

Joint shipment consolidation and inventory decisions in a two-stage distribution system

This study is motivated by a problem that an industrial distributorship faced while distributing automotive spare parts to service and repair centers. Considering the problem encountered, we present an analytical model for joint inventory and shipment consolidation decisions in a two-stage distribution system with a single distribution center, multiple non-identical retailers, and an outside supplier. The retailers face stochastic end-customer demand and use continuous review to replenish inventories. On the other hand, the distribution center uses a periodic review policy and employs a time-based shipment consolidation policy to dispatch retailers’ accumulated orders at the end of each consolidation cycle. We present an exact optimization technique to compute the optimal replenishment quantity at the distribution center, order-up-to level at retailers, and a shipment consolidation cycle length to measure the effects of inventory at retailers on the overall performance. Finally, we perform numerical experiments to measure the impact of various parameters on the overall distribution system.     

A near-optimal database allocation for reducing the average waiting time in the grid computing environment

In a grid computing environment, a great many users may access the same database simultaneously. To reduce the average waiting time for all users, a grid designer usually replicates the frequently accessed database among nodes based on the load balance heuristic. On the other hand, users may raise identical queries regarding an issue of interest, e.g., stock information, on a database and each of the queries will be directed to any node having a replica of that database. That is, the same answer will be determined by multiple nodes. Consequently, there exist two shortcomings of poor data sharing and duplicate calculations if the database is not replicated and allocated adequately. In this paper, we aim to minimize average waiting time and try to overcome the two shortcomings by performing database allocation over multiple nodes without any replication. The main idea behind the proposed method is to map the original problem to the Euclidean space Rⁿ and to solve the mapped problem in Rⁿ by a gradient-based optimization technique. The theoretical analyses ensure that the proposed method can converge linearly and achieve near-optimal results.     

Integrated inventory control and inspection policies with deterministic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. Both the order quantity and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks are set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.     

Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level

We study an EOQ inventory model with demand rate and holding cost rate per unit time, both potentially dependent on the stock level. The ordering cost, the holding cost and the gross profit from the sale of the item are considered. The objective is to maximize the average profit per unit time. We present the analytical formulation of the problem and demonstrate the existence and uniqueness of the optimal cycle time, giving a numerical algorithm to obtain it. Moreover, we provide two fundamental theoretical results: a rule to check when a given cycle time is the optimal policy, and a necessary and sufficient condition for the profitability of the system. Several EOQ models analyzed by other authors are particular cases of the one here studied. We present some numerical examples to illustrate the proposed algorithm and analyze the sensitivity of the optimal solution with respect to changes in various parameters of the system.     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

A partially integrated production-inventory model with interval valued inventory costs,variable demand and flexible reliability

This paper formulates a production-inventory model to investigate the effects of partially integrated production and marketing policy of a manufacturing firm. Demand is assumed to be variable and dependent on the selling price and marketing cost. Also, different inventory costs are considered as interval valued. Shortages are permitted and partially backlogged with a rate dependent on the waiting time. Considering that manufacturing process generates defective units four possible cases have been identified and studied. Basically, the optimization problems (maximization problem for Marketing department and minimization problems for Production and Research & Development departments) have been formulated and solved. For solving these optimization problems, an efficient soft computing algorithm based on Particle Swarm Optimization-Constriction factor (PSO-CO) is proposed. In order to illustrate and validate the production-inventory model a numerical example is solved. Finally, a sensitivity analysis is done to study the effect of changes of different system parameters on optimal policies.     

A VNS approach to multi-location inventory redistribution with vehicle routing

This paper analyzes a two-echelon inventory problem with uncertain demand, where perishable products are distributed from a central warehouse to retail stores. To better deal with uncertainty, we propose a model in which, at a certain point in time during the operation time window, transshipments between retail stores are allowed in order to re-balance the inventories. The model captures the following decisions: (i) which retail stores are included in re-balancing, (ii) in which sequence will they be visited, (iii) what are the optimal initial delivery and transshipment quantities and (iv) what is the optimal timing for transshipments. The model is solved with variable neighborhood search, which is extended with a dynamic programming sub-routine to handle inventory allocation. We compare our results with similar models from literature. The results show a noticeable improvement over the standard “single-order, no transshipments” policy even though only the inventory level of the visited customer is known. The transshipment quantities have to be determined without knowledge of the inventories of all other customers.     

Stochastic skill-based manpower allocation in a cellular manufacturing system

In this paper, stochastic skill-based manpower allocation problem is addressed, where operation times and customer demand are uncertain. A four-phased hierarchical methodology is developed. Egilmez and Süer's [1] stochastic general manpower allocation problem is extended such that each worker's individual performance is considered for a more accurate manpower allocation to manufacturing cells to maximize the production rate. The proposed methodology optimized the manpower levels, product-cell formations and individual worker assignment hierarchically with respect to a specified risk level. Three stochastic nonlinear mathematical models were developed to deal with manpower level determination, cell loading and individual worker assignment phases. In all models, processing times and demand were assumed to be normally distributed. Firstly, alternative configurations were generated. Secondly, IID sampling and statistical analysis were utilized to convert probabilistic demand into probabilistic capacity requirements. Thirdly, stochastic manpower allocation was performed and products were loaded to cells. In the final phase, individual worker assignments were performed. The proposed methodology was illustrated with an example problem drawn from a real manufacturing company. The hierarchical approach allows decision makers to perform manpower level determination, cell loading and individual worker assignment with respect to the desired risk level. The main contribution of this approach is that each worker's expected and standard deviation of processing time on each operation is considered individually to optimize the manpower assignment to cells and maximize the manufacturing system production rate within a hierarchical robust optimization approach.     

Stability condition for m/d/l retrial queuing system with a limited waiting time

A stability condition is derived for a queueing system with a Poisson input with parameter λ and constant service time τ. If the virtual waiting time is less than a constant a, then the demand can be serviced; otherwise, it is repeated in exponentially distributed time or is lost with a probability q >- 0. Translated from Kibemetika i Sisternnyi Anaiii. No. 2, pp. 184–186, March–April, 2000.     

A mixed inventory model with variable lead time and random back-order rate

In this paper, we study the determination of the optimal lead time, reorder point and order quantity considering that the back-order probability of a demand made during a stock-out period depends on the interval from the moment in which the order is placed until the next replenishment. Two models are analysed for the specification of the back-order probability: exponential functions and piecewise constant functions. The distribution of the lead time demand is assumed to be Poisson. An algorithm for the determination of the optimal order quantity, reorder point and lead time is given. A numerical example is presented to illustrate the results.     

An integrated inventory model with capacity constraint and order-size dependent trade credit

Trade credit has many forms in today’s business practice. The most common form of trade credit policy that is used to encourage retailers to buy larger quantities is order-size dependent. When the number of ordered units exceeds the capacity of the own warehouse, an additional rented warehouse is required to store the excess units. Therefore, to incorporate the concept of order-size dependent trade credit and limited storage capacity, we proposed an integrated inventory model with capacity constraint and a permissible delay payment period that is order-size dependent. In addition, the unit production cost, which is a function of the production rate, is considered. Three theorems and an algorithm are developed to determine the optimal production and replenishment policies for both the supplier and the retailer. Finally, numerical examples are presented to illustrate the solution procedure and the sensitivity analyses of some key parameters are provided to demonstrate the proposed model.     

An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit

Under a business trading environment, it is common for the trade credit to depend on the order size. Therefore, it is important to discuss the single-supplier and single-buyer supply chain problem which includes order-size dependent trade credit. In this study, an integrated inventory model with a price sensitive demand rate, determining jointly economic lot size of the buyer’s ordering and the supplier’s production batch, are developed to maximize the total profit per unit time. An efficient algorithm is provided to obtain the optimal solution, and then numerical examples are presented to illustrate the theoretical results. Finally, the comparison between whether an optimal solution is jointly or independently determined is also provided.     

A numerical solution for a two-stage production and inventory system with random demand arrivals

This paper is about the study of a production lot sizing problem consisting of customers, one retailer, and one manufacturer. Demand from customers arrives randomly at a retailer one unit at a time. The retailer replenishes inventory from the manufacturer upon receiving a customer's order after its inventory depleted to zero. The manufacturer's production rate is assumed to be a finite constant. A production cycle starts when the manufacturer's inventory falls to or below zero and stops when its on-hand inventory reaches its optimal level. During the uptime in a production cycle, inventory is being built while randomly arriving orders from retailer are being fulfilled. The order arrival times from customers are independently and identically distributed, hence the inventory processes at both the manufacturer and the retailer become a renewal process that is difficult to solve analytically for a general distribution of order arrival time. Therefore, a numerical approach is used in developing a search procedure to obtain the optimal solution to the problem. Employing such a numerical approach, we also investigate how optimal solutions in different cases will change over the spectrum of some key parameters of the problem.     

A general and optimal approach for three inventory models with a linear trend in demand

This study provides a general and simple algorithm to obtain an optimal solution for three inventory models with a replenishment batching policy, production batching policy, and an integrated replenishment/production batching policy in a manufacturing system, under a finite time horizon and linear trend in demand. This study determines the replenishment or production schedule with one general equation for these three problems and provides fully theoretical proofs for relaxing some of the conjectures in previous studies. A general and explicit procedure to derive the optimal solution for these three inventory models is presented, while considering both linearly increasing and decreasing demands. In addition, demonstrations of applicability are performed.     

Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering

A variable demand inventory model was developed for minimizing inventory cost, treating the holding and ordering costs and demand as independent fuzzy variables. Thereafter, backordering cost was also considered as an independent fuzzy variable. Fuzzy expected value model and fuzzy dependent chance programming model were constructed to find the optimal economic order quantity, which would minimize the fuzzy expected value of the total cost, so that the credibility of the total cost not exceeding a certain budget level was maximized. Optimization was carried out using genetic algorithms and particle swarm optimization algorithm, and their performances were compared. The developed model was found to be efficient not only in one artificial case study but also in two data sets collected from the industries. Therefore, this model could solve real-world problems, too.     

Simultaneous coordination of order quantity and reorder point in a two-stage supply chain

In this paper, we investigate the simultaneous coordination of order quantity and reorder point in a two-stage supply chain (SC). While coordination of order quantity has received much attention in the supply chain management literature, coordination of the reorder point has been less-studied. The retailer's reorder point has a direct impact on product availability and customer service level (CSL) and therefore has a great impact on SC profitability. Our proposed model adopts a two-stage SC with stochastic demand and lead times over multiple periods. The proposed coordination model assures global optimization of order quantity–reorder point decisions. Using a pricing scheme with a discount factor, we extract conditions in which both downstream and upstream members have sufficient motivation to participate in the coordination scheme. Numerical experiments demonstrate that the proposed model can achieve channel coordination. Results of the modeling and analyses show that coordination of both reorder point and order quantity can lead to increased SC profitability as well as CSL improvement.     

The EOQ repair and waste disposal model with switching costs

This paper addresses the problem of determining the optimal batch sizes for production and recovery in an EOQ (economic order/production quantity) repair and waste disposal model context. This paper assumes that a first shop is manufacturing new products as well as repairing products used by a second shop. The used products can either be stored in the second shop and then be brought back to the first shop in an approach used to reduce inventory costs, or be disposed outside the system. The works available in the literature assumed a general time interval and ignored the very first time interval where no repair runs are performed. This assumption resulted in an over estimation of the average inventory level and subsequently the holding cost. These works also have not accounted for switching costs when alternating between production and recovery runs, which are common when switching among products or jobs in a manufacturing facility. This paper addresses these two limitations. Mathematical models are developed with numerical examples presented and results discussed.     

Solving single-product economic lot-sizing problem with non-increasing setup cost,constant capacity and convex inventory cost in O(N log N) time

This paper considers an economic lot sizing model with constant capacity, non-increasing setup cost, and convex inventory cost function. Algorithms with computational time of O(N×TD_N)have been developed for solving the model, where N is the number of planning periods and TD_N is the total demand. This study partially characterizes the optimal planning structure of the model. A new efficient algorithm with computational time of O(N log N) has also been developed based on the partial optimal structure. Moreover, computational study demonstrates that the new algorithm is efficient.     

Continuous review inventory model with controllable lead time,lost sales rate and order processing cost when the received quantity is uncertain

In practice the quantity received may not match the quantity ordered due to worker's strike, rejection during inspection, damage during transportation, human errors in counting, etc. Accordingly, the managers often must make decisions under uncertain quantity received circumstances. In this study, we investigate the continuous review inventory model with shortages include the case where the quantity received is uncertain, in which the lead time, lost sales rate and order processing cost are decision variables. Here, we consider the lead time crashing cost is an exponential function of lead time, and the order processing cost and lost sales rate are logarithmic functions of capital investment. The objective of this study is to minimize the total relevant cost by simultaneously optimizing the order quantity, lost sales rate and order processing cost. In addition, an efficient algorithm is developed to determine the optimal policy, and our approach is illustrated through a numerical example. From the results of numerical example, it can be shown that, the significant savings can be achieved through the reductions of order processing cost and lost sales rate.